1250-1750-word (+ Works Cited)

36Review of Professional Management, Volume 12, Issue 1 (January-June-2014)

Asymptotic Limit of Consumption and Threshold Level of I ncome with reference to I ndore City

Shubhangi Jore*, R. C. Sharma**

Abstract

The concept of asymptotic level of consumption is defined as increase in consumption of a

commodity with income but only up to a level and then after reaching a maximum level it

becomes stable irrespective of income. Especially, food consumption stops increasing with an

increase in income because of the limitation associated with digestive system. It is observed that

empirical study on maximum food consumption as well as threshold income have not been done

on Indian situation. Growing need was felt to conduct an academic study for Indore city with

respect to their food consumption pattern to derive the maximum potential level of consumption

termed as asymptotic limit of consumption as well as threshold level of income. Data from

Indore city are collected on the basis of a sample of size of 714 household units. Then, the

asymptotic limit of consumption and threshold level of income have been estimated using

reciprocal transformation method. In all the cases, there exists significant positive relationship

between income and food consumption. Hence, the first hypothesis, β 1 > 0, was accepted at 5%

level of significance for food commodities rice, wheat, other cereals, pulses, dairy products,

edible oil, eggs and other food items. This indicates that increase in income results in increase in

food consumption derived from the above mentioned food categories. Consumption of these food

categories seems to have reasonable prospect for expansion although at a lower rate, especially

in the case of animal products. The analysis suggests that consumption is still well below

saturation level(asymptotic level) and that appreciable increases are still possible.

Key Words: Asymptotic Limit; Threshold Level; Indore city; Food Consumption

*Ms. Shubhangi Jore

Assistant Professor in Operations, Prestige

Institute of Management and Research,

Devi Ahilya University, Indore, India

**Mr. R.C. Sharma

Head-Department of Management, Central

University of Rajasthan, Kishangarh

(Ajmer)305801, Rajasthan, India

I ntroduction

The concept of asymptotic level of consumption is

defined as an increase in consumption of a commodity

with an increase in income only up to maximum level

after which it becomes stable irrespective of income.

This maximum level of consumption is defined as the

limit of consumption and termed as asymptotic limit

(Gujarati, 2007). For example, saturation level of

consumption of any food item can be explained as

the physical consumption of food which is limited by

the capacity of the human digestive system. Yet,

37Review of Professional Management, Volume 12, Issue 1 (January-June-2014)

expenditure on food is not so strict ly limited as it is

possible for well- fed count r ies w ith suf f icient

purchasing power to go on spending more and more

in order to obtain a more desirable quality and variety

of food. Additionally, consumption expenditure might

be increasing due to wastage by the rich countries.

The paper also assumes that families below threshold

level of income do not purchase food from the market

due to lack of purchasing power. Thus, the threshold

level of income is the crit ical level at which the

relationship between consumption and income is

established. To est imate the asymptot ic limit of

consumption as well as the threshold level of income

for a particular city like Indore at micro level for

regional marketing strategies are of much interest.

Any at tempts to est imate these asymptot ic or

saturation levels of consumption and the threshold

level of income must involve an element of subjective

judgment but in exercising such judgment it is useful

to have some objectively determined data as a check.

Review of Literature

The econometric estimation of asymptotic limit of

consumption and the threshold level of income are

gaining interest in recent econometric contributions.

Moreover, there have also been significant advances

in the methodology of estimation of maximum potential

level of consumption. The reciprocal transformation

model in the estimation of relevant parameters on

the basis of cross-sectional data is a methodological

refinements of tradit ional estimation methods. I ts

significant in policy formulations is mainly determined

by how a reciprocal transformation model is specified

and estimated.

The changing demographic profiles, increasing income

levels, urbanization, technology, globalization and a

free flow of ideas from within and outside the country,

have brought about a dramatic shift in consumer tastes

and preferences ult imately ef fect ing the food

consumption pattern (Kumar and Sarkar, 2008).

Although recently, the study of food consumption is

approached with the integrated perspective (Petrovici

et al., 2005), init ially it comprised of fragmented

studies (Ritson et al., 1986). In the past, there have

been evidences in the evolution of food consumption

in European countries analyzed by several authors

(Besch, 1993; Blandford, 1984; Frank and Wheelock,

1988; Gracia and Albisu, 2001) Meulenberg and

Vianne, (1993) Ritson and Hutchins, (1991) Wheelock

and Frank (1989), outline some of the important

findings as follows: trend of decreased the proportion

of expenditure allocated to food, food consumption

reached the maximum level in total food category, an

increase in proportion of take away food and there

was a shift in the food consumption pattern. These

trends indicated that economic growth was common

to all the European count r ies. The reason for

consumption reaching the maximum level in the total

food category was that people wanted to eat better

as their daily intake requirements diminished and in

wealthy countries generally quantity surpassed by

quality concerns. The proportion of shift in food

consumption structure was not homogenous for all

the European Countries, it varied depending on their

cultural and historical evolutions. The last trend of

increase in proportion of food take away was almost

common for all countries but it varied in its intensity

among countries and with labor circumstances.

The economic theory and the consumer behaviour

suggest three important factors responsible for annual

variation in per capita food expenditure which is

explained by neoclassical methods of est imating

household demand for food. The three important

factors are household real income, product price, and

the prices of substitute products including nonfood

products (Deaton and Muellbauer, 1980 and Gracia et

al., 1998) and two more added by Elsner and Hartmann

(1997) as preferences and socio-demographic factors.

The models that are based only on these three factors

are quite powerful and impressive in predict ing

(Connor, 1994).

In the earlier studies, Adrian and Daniel (1976)

studied the impact of socioeconomic characteristics

of household and its constituents on consumption of

protein, carbohydrate, fat, vitamin A, calcium, iron,

thiamine and vitamin C. Socioeconomic factors

considered included income, degree of urbanization,

race educational attainment of the homemaker, stage

of the household in the family life cycle, family size,

meal adjustment and the employment status of the

homemaker. The study showed a posit ive impact on

the consumption of all nutrients except carbohydrate.

I t was also revealed that the nutrient consumption

responsiveness to income was relatively small.

38Review of Professional Management, Volume 12, Issue 1 (January-June-2014)

Several studies have focused on specifying the

in f luence of household incom e and ot her

socioeconomic characteristics on nutrient consumption

but most of these have been limited to localized areas

or particular groups of people (Babcock, Einstein and

Horstein, Kel-say, Madden and Yoder). Generally, these

studies noted signif icant variat ions in nut rient

consumption with respect to income, education, and

race. Saxon (1975) has used the model which

explores the effects of prices and substitutes on the

consumption of certain products. The results using

these models incorporated prices of substitutes as

explanatory variables. I t has showed that a rise in

the price of beef appeared to be a factor contributing

to increase consumption of pork. The results revealed

that prices of pork and chicken did not affect the

elasticities for beef during the period 1963-1972 while

the price of beef had signif icant effect on the

consumption of both pork and chicken.

Saxon (1975) has further studied the saturation level

of food part icularly in Japan. During the period

considered, t here were evidences of people

approaching or reaching a level of saturation in food

consumption taken as a whole measured in calories.

I t revealed that this saturation level of food is being

approached or has reached in most of the economically

advanced countries. The estimation of maximum

potential level or asymptotic level of consumption is

meaningful in conjunction with other evidence in

making some assessment of the likely growth or

contraction in the region of Asia. I t is generally

acknowledged that income and the price are by no

way the exclusive determinants of food consumption,

although they are thought to be normally the easiest

to measure. Other than income, the price and some

additional factors influencing food consumption may

be grouped, according to Saxon, under five headings.

The headings go as (i) physical need (ii) availability

(iii) changes in services (iv) tastes and (v) changes in

geographical distribution of population.

All the research mentioned above, suffered from the

limitat ion that they were confined to meet the

marketing requirement(s) of the countries other than

India. As such, growing need was felt to conduct an

academic study of Indore city with respect to their

food consumption pattern and to provide a maximum

potential level of consumption and threshold level of

income of the city. To fill in the gap, it is therefore,

useful at t h is j uncture t o examine t rends in

consumption patterns in Indore city at micro level and

deliberate on the potential of the food and agriculture

sector to meet demands and challenges posed by the

dynamic environment. The objective of the study is

to estimate asymptotic limit of food consumption and

to estimate the threshold level of income at micro

level in Indore city.

Research Methodology

One of the methods to estimate the asymptotic limit

of consumption and threshold level of income is named

reciprocal transformation method. The model is of

the form given in equation (1).

X i

1 Y

i = βββββ

1 + βββββ

2 + u i

( )

where … (1)

Y i = Food Consumption in kcal per capita per day for

ith country

X i = GDP at factor cost in $ for ith country

This model is non-linear in the variable X because it

enters inversely or reciprocally, the model is linear in

βββββ 1 and βββββ

2 and is therefore a linear regression model.

The model has built in itself an asymptote or limit

value that the dependent variable will take when the

value of X variable increases indefinitely. As X

increases indefinitely, the term

X i

1 βββββ

2 ( )

approaches zero and Y approaches the limit ing or

asymptotic value of βββββ 1 . I t is clear that as income

becomes very large, consumption of any product will

tend to level out. The relationship is unlikely to be as

simple as suggested by this formula. In the first place,

it assumes that income is the sole explanatory

variable, and in the second place, saturation only

approaches as income approaches infinity.

39Review of Professional Management, Volume 12, Issue 1 (January-June-2014)

Empirical Analysis

Data from Indore city are collected with a sample of

size of 714 household units. 94 percent of the

respondents are headed by males while only 6

percent are headed by females. Families on an

average are headed by a middle aged person with a

mean age of 48 years. The occupation of head of the

family is 57 percent service, 36 percent business, 5

percent retired and only 2 percent are headed with

no males. Families considered for analysis reported

that wives of head of the family are 69 percent

housewives, 14 percent in service, 1 percent retired

while rest are families with no male head. The

qualification of head of family is 45 percent graduates,

40 percent post graduates, one percent post doctorate,

12 percent high school and rest 2 percent below high

school. Most of families are with a household size of

4 members while an average household size of 5

members. The average annual income of families is

Rs. 4,06,071 while there are maximum numbers of

families earning a total annual income of Rs. 3, 00,

000. On an average the considered families spend

Rs. 83,350 per year on food with an average 32

percentage share of their income on food.

The relation between income and food consumption

is tested init ially by plot t ing the scat ter plot

(Appendix) . There is an indication of increase in

consumption of total food expenditure, rice, wheat,

other cereals, pulses, milk, vegetables, fruits, dairy

products, oil, sugar, tea, coffee, meat / chicken, fish,

eggs and other food with an increase in income. From

the scat ter plot it can be said that the rise in

consumption is not directly proportional to the rise in

income. The consumption increases initially and slows

down later with increase in income. Estimation of

asymptotic limit of household food consumption and

threshold level of income at micro level in Indore city

is done using reciprocal transformation model given

by equation (1) where, Y i denotes consumption of

commodity of food in Rupees of a family (household),

X i represents annual income of a family (household)

in Rupees to estimate parameters involved. The

Ramsey’s RESET test is applied to specify the model.

The table 1 reflects the F-statistics used to identify

specification error using Ramsey’s RESET test and

the parameters.

From the table 1, the RESET test indicates that F-

values are lower than the crit ical value at 1 percent

level of significance for the food commodities such as

rice, wheat, other cereals, pulses, dairy products,

edible oil, eggs and other food items and hence do

not contain any specification error.

Except for the food categories , milk, vegetables, fruits,

sugar, tea, coffee, meat/chicken and fish, there does

not exists any specification error in the model. Hence

reciprocal transformation regression model is run and

parameters are estimated for food categories which

do not report specificat ion error. The est imated

maximum potential level (asymptotic limit) of food

consumption and the threshold level of income for

food categories with no specif icat ion error are

reported in the table 1. In all cases where there

existed significant relationship between income and

food consum pt ion, t here exist ed a posi t ive

relationship. Hence the first hypothesis, β 1 > 0, was

accepted at 5% level of signif icance for food

commodities rice, wheat, other cereals, pulses, dairy

products, edible oil, eggs and other food items. This

indicates that increase in income results in increase

in food consumpt ion der ived f rom the above

mentioned food categories.

The food category of other food items is showing the

highest asymptotic limit of Rs. 22, 134 amongst the

reported food items and consumed by 90 percent of

families. With increase in income in Indore, people

are increasingly spending on the food items other than

the items considered for the analysis. These other

items may include ready to eat food items, packaged

food items, meals taken away from home (not

prepared at home) etc. As the percentage of working

females has increased since last decade, the habit of

eating out, using ready to eat food items (ready food

items) and packaged food items have increased and

hence repor t ed h ighest asym pt ot ic l im i t of

consumption at micro level. The threshold level of

income for this food category is Rs. 78, 860 which is

again highest amongst the reported food items. This

indicates that spending on other food items is mostly

affordable by higher-middle-income class families.

Of the reported food items in the table 1, the next

food commodity that has achieved a maximum

potential level of consumption is dairy products with

an asymptotic limit of Rs. 8, 733 and threshold level

of income Rs. 64, 581. Dairy products include yogurt,

cheese, butter, cottage cheese (paneer), chakka

40Review of Professional Management, Volume 12, Issue 1 (January-June-2014)

(water- less yogurt used in the preparat ion of

Shreekhand, one of the popular sweets in the city)

and other milk products. Dairy products are consumed

by 93 percent of families of the considered sample

size. Dairy products are high valued products which

are consumed increasingly with an increase in income,

High threshold level of income is an indication of

consumption again by a higher-middle-income class

of families.

Table 1: Specification Error Test, Asymptotic Limit of Consumption and Threshold Level of I ncome:

Micro Data Analysis

Food RESET Asymptotic Threshold

Commodity test limit of level of

F-statistic consum t Income

ption βββββ 1

statistic βββββ 2

βββββ 2

/ βββββ 1

Rice 2.59 3698.87 21.51 -121930192.19 32964.18

Wheat 1.97 5258.95 30.44 -96699671.33 18387.64

Other Cereals 3.62 1073.68 13.91 -46340203.07 43160.09

Pulses 3.35 4013.02 21.61 -130003683.30 32395.50

Milk 18.06 * - - - -

Vegetables 6.04 * - - - -

Fruits 36.97 * - - - -

Dairy Products 3.25 8732.61 6.79 -563961873.13 64581.15

Edible Oil 2.06 8000.35 7.78 -347651692.73 43454.58

Sugar 4.93 * - - - -

Tea 7.16 * - - - -

Coffee 7.33 * - - - -

Meat/ Chicken 5.00 * - - - -

Fish 5.42 * - - - -

Eggs 4.08 1423.79 8.73 -72419866.01 50864.23

Other Food 1.14 22134.10 2.96 -1745507587.57 78860.44

Total Food 48.24 * - - - -

Source : Authors calculation using Ramsey’s RESET test and reciprocal transformation model (1)

Note : * significant at 1 % level of significance with crit ical value of F-statistic F 0.01 (2, “)

= 4.61.

41Review of Professional Management, Volume 12, Issue 1 (January-June-2014)

Edible oil is the category of food which has attained

an asymptotic limit of Rs. 8, 000 and threshold level

Rs. 43, 455. With increase in income, consumption of

edible oil is also increasing and has attained a third

posit ion in achieving maximum potential limit of

consumption (amongst the reported food items) in

Indore city. The threshold is not at the third place

and hence oil is consumed by most of the families

irrespective of any class of income.

The food item, wheat has attained a maximum

potential level of Rs. 5, 259 and threshold level of Rs.

18, 388. The low threshold of the commodity is the

indication of consumption of wheat by even low

income-class people. The consumption of wheat is

stabilized at the asymptotic level which is moderate,

not much low and not high. I rrespective of the income

class, families in Indore city are consuming wheat

which is one of the staple food commodit ies.

Traditionally, people in the city purchase wheat once

in a year somewhere during March to June and store

it for making use over a year. Wheat is the basic food

item which is consumed mainly in the main course by

every class of family. With increase in income, the

consumption of wheat increases to a moderate size

and stabilizes.

The category of staple food, pulses, rice, and other

cereals stabilize respectively with an asymptotic limit

of Rs. 4013, Rs. 3699 and Rs. 1074. I t is considered

that pulses (dal ) is a high source of protein and

tradit ionally it is consumed commonly with rice not

only in the city I ndore but also in the country

irrespective of any season, religion, culture or income-

class. While consumption of other cereals like corn

(makka), jwar, bajara etc. stabilize at a low asymptotic

limit. This category of food is mostly consumed by

the people in rural area and hence its consumption

does not increase much with increase in income in

the Indore city. The category of other cereals is a

special type of food category which is not so common

in urban areas and is consumed very less frequently

only by some of the categories of the people. Other

cereals food category is consumed by 89 percent of

families while rice and pulses are consumed by all

families in the sample.

Eggs are consumed by 43 percent of families and

attain a maximum potential level of Rs. 1, 424 and

threshold level of Rs. 50, 864. Less than half of the

considered sample size consume this food commodity

and attains a low asymptotic level of consumption.

The reason may be that this is consumed by a

particular group of people. Unlike the staple food,

consumed uncommonly in the city and its consumption

depends on the season (especially in winter and

rainy), religion, culture. The threshold is not much

low and indicates the consumption of the commodity

by moderate income-class people.

Conclusion

Micro data collected from Indore city is characterized

on an aggregate by households which are middle

aged, graduates male heading with majority of service

class families. On an average families are headed by

graduate males with a modal family size of four

members and average family size of five members.

This indicates the families in general are male headed

and there still exists a culture of joint family in the

city. Most of the families are middle income-class and

spend on an average Rs. 83, 350 on food annually

with an average 32 percent share of their income on

food.

In general, consumption of food has not yet reached

a plateau at micro level while there are some

differences in different food categories. There is a

general tendency of people in Indore to spend on other

type of food items which may include ready to eat

food items, packaged food items, meals take away

(not prepared at home) etc. As the percentage of

working females has increased since last decade, the

habit of eating out, using ready to eat food items

(ready food items), and packaged food items has

increased and hence reported highest asymptotic limit

of consumption at micro level. A High threshold level

for this food category is the indication of consumption

of other food items by the higher-middle-income class

families. Consumption of dairy products and edible

oil (fats) are also increasing with an increase in income

and are appearing below the saturat ion level.

Consumption of these food categories seems to have

reasonable prospect for expansion although at a lower

rate. Especially in the case of animal products the

analysis suggests that consumption is still well below

saturation level and that appreciable increases are

still possible.

42Review of Professional Management, Volume 12, Issue 1 (January-June-2014)

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